On Reconstructing Configurations of Points in ℙ2 from a Joint Distribution of Invariants (original) (raw)

Abstract.

Consider the diagonal action of the projective group PGL3 on n copies of ℙ2. In addition, consider the action of the symmetric group Σ n by permuting the copies. In this paper we find a set of generators for the invariant field of the combined group Σ n ×PGL3. As the main application, we obtain a reconstruction principle for point configurations in ℙ2 from their sub-configurations of five points. Finally, we address the question of how such reconstruction principles pass down to subgroups.

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Authors and Affiliations

1. Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, IN, 47907, USA
   Mireille Boutin
2. Technische Universität München, Zentrum Mathematik - M11, Boltzmannstrasse 3, 85748, Garching, Germany
   Gregor Kemper

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1. Mireille Boutin
2. Gregor Kemper

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Correspondence toMireille Boutin.

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Boutin, M., Kemper, G. On Reconstructing Configurations of Points in ℙ2 from a Joint Distribution of Invariants.AAECC 15, 361–391 (2005). https://doi.org/10.1007/s00200-004-0168-2

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• Received: 05 April 2004
• Revised: 23 September 2004
• Published: 22 December 2004
• Issue date: April 2005
• DOI: https://doi.org/10.1007/s00200-004-0168-2

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